Problem: Simplify the following expression: $z = \dfrac{10}{7x} + \dfrac{7}{8x}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7x$ and $8x$ $\lcm(7x, 8x) = 56x$ $ z = \dfrac{8}{8} \cdot \dfrac{10}{7x} + \dfrac{7}{7} \cdot \dfrac{7}{8x} $ $z = \dfrac{80}{56x} + \dfrac{49}{56x}$ $z = \dfrac{80 +49}{56x}$ $z = \dfrac{129}{56x}$